The RPM'sRPMs would certainly increase but the mechanical components would be prevented from exceeding maximum RPM'sRPMs by a rev-limiter.
Rev-limiters are built into the ECU (computer) of the car. When an engine is spinning at it'sits maximum RPM set by the manufacturer, the ECU will not send a spark to particular cylinders to prevent the engine from spinning faster and potentially damaging itself.
If a rev-limiter were not in place the engine would have a high likely-hood of experiencing valve to piston contact. Valve to piston contact occurs when the valve cannot close quickly enough to get out of the way of the piston on an upstroke. The result is catastrophic with a hole being punched in the top of the piston by the lingering valve. Results of this type of failure will vary. Imagine loose bits of aluminum and steel flying around inside of an engine at or beyond it'sits maximum RPM'sRPMs and you get the idea.
This applies to modern cars with rev-limiters. Older vehicles will not have this self-protection device. I defer to an expert with more information regarding when rev-limiters began to be implemented by the manufacturers to edit this answer with some of that information and remove this paragraph. ThanksThanks.